Talk:Special relativity/Archive 23

Archive 20

Archive 21

Archive 22

Archive 23

Latest suggestion

In pre-relativistic physics, measured distances ($\Delta x$) and time lapses ($\Delta t$) between events were assumed to be independent invariants, and there were just, then only recently, emerging ideas that these measurements could change when taken in another frame. In special relativity the intrinsic interweaving of spatial and temporal coordinates fundamentally destroys this separate invariance, supported from everyday life, leaving just the difference of the squares of these quantities, denoted as $\Delta s^{2}$, as invariant. The invariance of this quantity can be deduced in a straightforward manner from the Lorentz transform.

$\Delta s^{2}\;{\overset {def}{=}}\;c^{2}\Delta t^{2}-\Delta x^{2}.$

Expanding the linear spatial distance $\Delta x$ with Pythagoras' theorem makes the invariant interval applicable to the general transformation between any two Cartesian inertial frames, which may include, in addition to the standard Lorentz transformation, rotations, translation in space, and translations in time (i.e. a Poincaré transformation).

$\Delta s^{2}=c^{2}\Delta t^{2}-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2}).$

References

Notes

Rationale:

• Making $\Delta x$ and $\Delta t$ explicit makes it easier to hint to the special feature of "minus"(!) in the Minkowski metric. I think this remains hard enough to keep in mind when looking at spacetime diagrams, when the "obvious sum" of two triangle sides is "shorter" than the "longest" side. Furthermore, I believe reasons to assume non-invariance did emerge then.
• Recalculating the Euclidean "unique linear spatial distance" via "Pythagoras" is no "re-definition", superseding the previous one. I inserted the parens and exchanged the "-"s for making Pythagoras more obvious. I settle on agreeing on disagreement.

May I ask that you include as much as is to your liking, I consider in any case my ideas as sufficiently considered. Purgy (talk) 09:54, 11 November 2018 (UTC)

Mentioning asides: Shouldn't this section be moved up to Consequences ..., too. More distant: I was very proud about me writing in the lead the "causing - caused" play on words, because I hoped someone were reminded of Wheeler's "how to move - how to curve", but I fully understand that it might not be good English. :) Sorry, Purgy (talk) 11:04, 11 November 2018 (UTC)

Much improved! You've bypassed my objections to $\Delta x^{2}$ and $\Delta t^{2}$, but I still think it is a bit verbose and overly coy in hinting at (but not actually describing) the "emerging ideas" (i.e. Lorentz, Poincaré). Let me re-read some relevant chapters in Arthur I. Miller's Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905-1911) before responding. You make me WORK! I'm still uncertain about Pythagoras. Prokaryotic Caspase Homolog (talk) 12:23, 11 November 2018 (UTC)

OK, how about this? There is absolutely no need to (hint, hint) at the "emerging ideas that these measurements could change when taken in another frame" since those ideas had already been quickly suggested in the Introduction, and a link to History of special relativity had been provided.

In pre-relativistic physics, measured distances ($\Delta x,\Delta y,\Delta z$) and time lapses ($\Delta t$) between events were assumed to be independent invariants. In special relativity, the intrinsic interweaving of spatial and temporal coordinates fundamentally destroys these separate invariances, supported from everyday life, leaving just the difference of the squared time lapse and the summed squares of the spatial quantities, denoted as $\Delta s^{2}$, as invariant:

$\Delta s^{2}\;{\overset {def}{=}}\;c^{2}\Delta t^{2}-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2}).$

The invariance of this quantity can be deduced from the Lorentz transform. This invariant interval, related to the Pythagorean theorem, is in fact applicable to the general transformation between any two Cartesian inertial frames, which may include, in addition to the standard Lorentz transformation, rotations, translation in space, and translations in time (i.e. a Poincaré transformation).

For simplified scenarios such as in the analysis of spacetime diagrams, a reduced-dimensionality form of the invariant interval is often employed:

$\Delta s^{2}\,=\,c^{2}\Delta t^{2}-\Delta x^{2}.$

Demonstrating that the interval is invariant is straightforward for the two dimensional case and with frames in standard configuration:

References

Notes

Prokaryotic Caspase Homolog (talk) 08:44, 13 November 2018 (UTC)

Only because you asked for it explicitly:

Omitting the (hint, hint) is fine if hinting was already done (note the "are" in the text now); Euclidean metric (= Pythagoras = SUM of squares) is well known, but I would avoid mentioning Pythagoras, when the spacetime metric (= DIFF of squares) is addressed nearby. How about renaming the first occurrence of $\Delta x$ to $\Delta r$? I simply like the ultimately terse definition of the spacetime metric, in contrast to the Euclidean metric, as the difference of $c^{2}\Delta t^{2}$ and $\Delta r^{2}$ much better than the one with a boring list of components (x,y,z). Orthogonal decomposition of a strictly 1-dim property into three components is no rocket science. Stripped by all refs, and cramming in some wild beasts to put into footnotes or to annihilate totally, this would look like:

In pre-relativistic physics, measured distances ($\Delta r$) and time lapses ($\Delta t$) between events are independent invariants. In special relativity, the intrinsic interweaving of spatial and temporal coordinates radically destroys these separate invariances, supported by everyday life experience; just the difference of the squared time lapse and the squared spatial distance, denoted as $\Delta s^{2}$, remains as the invariant spacetime interval, demonstrating a fundamental discrepancy between Euclidean and spacetime distances.

$\Delta s^{2}\;{\overset {def}{=}}\;c^{2}\Delta t^{2}-\Delta r^{2}.$

In three spatial dimensions $\Delta r^{2}$ can be expanded, according to Pythagoras' theorem, to

$\Delta s^{2}=c^{2}\Delta t^{2}-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2}),$

but in simplified 1-dimensional scenarios, as in the analysis of spacetime diagrams, the reduced-dimensionality form from above is often employed.

The invariance of the quantity $\Delta s^{2}$ is a property of the general Lorentz transform (also Poincaré transformation), making it an isometry of spacetime. The general Lorentz transform between any two Cartesian inertial frames covers, in extension to the standard Lorentz transform, which deals just with translations (Lorentz boosts) in x-direction, all other translations and reflections in space and in time, and also all transformations that keep the origin fixed (rotations).

Demonstrating ...

Objective measures of readability rank the various revised versions of the section, both yours and mine, about three grade levels more difficult to read than what is currently in place. Now, I believe that the first paragraph in any section needs to be maximally accessible, and the difference in difficulty level between the suggestions offered here and what is in place is quite dramatic. As I've stated before, a successful compromise leaves neither person completely happy. I will push as much as I can of your suggestions into main article space to achieve the additional precision of expression that you desire, but I insist on the readability of the first paragraph. Neither of us will get entirely what we want, but that's the nature of compromise... Prokaryotic Caspase Homolog (talk) 23:18, 13 November 2018 (UTC)

Who were I, if I dared to discuss the readability of my English babbling? There is just a faint doubt about the feasibility of "deep learned" programs significantly judging roughly five(!) sentences for their readability. I myself wrote about me cramming in topics I consider interesting for a reader passing by (sometimes with the intent to trivialize high brow lingo). I really feel honored by any small phrase of mine that makes it into an accepted version. I see my cramming in as just offering on topic window shopping for things I find didactically valuable and generally interesting.

Besides being quite satisfied as it stands, there is just this

$\Delta s^{2}=c^{2}\Delta t^{2}-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2}),$

or worse in its original form

$\Delta s^{2}=c^{2}\Delta t^{2}-\Delta x^{2}-\Delta y^{2}-\Delta z^{2},$

being preferred to

$\Delta s^{2}=c^{2}\Delta t^{2}-\Delta r^{2}$

that I do not understand. The latter version easily focuses on the important NEW temporo-spatial metric (with its minus), emphasizes the one-dimensionality of distance and is way shorter and therefore way more clearly laid out. I am convinced that the embedding of one-dimensional spatial distances in 3-dimensional Euclidean spaces via Pythagoras as

$-\Delta r^{2}=-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2})$

convinces even the faintest hearted. I admit that I am not a fan of this "standard configuration", with its dragging along of two parasitic spatial dimensions, adding nothing to substantial understanding at this level.

Please, do not bother to proselytize me to opinions in reliable sources, I really accept the versions that you find fit for WP. Purgy (talk) 10:10, 14 November 2018 (UTC)

Re recent edits

Re recent edits:

• Time dilation: To me it was important to hint to the "lifetime" of muons as an "expectation value", to contrast "high"- and "low"-speed muons, to emphasize "equality" in the respective rest frames, and, maybe not so important, to introduce "proper time". All four items negligible?
• Composition of velocities: I protest. It's about "transformations" of velocities to other frames: u to u'. The LT primarily transform coordinates, their "differential form" is unexplained jargon, the ubiquitous use of the word "addition of velocities" for this situation is abuse of language, be it widespread as it might. "Adding" velocities, as measured in different frames, is a categorical flaw, and each velocity measured in one frame, necessarily introduces another frame: the rest frame of the measured body. This is a delicate topic.
• Standard configuration: This, imho, had no encyclopedic value at all, if it were not for its necessity in introducing Minkowski diagrams, so I do not really understand the perceived emphasis put on it. My personal preference is to start with showing the boost-equations in (1+1) dimensions, generalize to (1+3) dimensions in matrix notation, and reduce the matrix again to "standard configuration". Maybe this would pay the rent in presenting the Thomas rotation, the transversal Doppler effect, ... Summing it up, I think from an encyclopedic POV it is more seminal to introduce the (3+1)-LT with β and γ, and stuff its matrix with 0s, than to put a priori importance on a "standard configuration", simply gained and well defined by these 0s.
• Two postulates: I do not understand the emphasis on this, too. It would be my first concern to derive from clunky postulates some most handy equations to proceed with the development of a closed theory. So why should any researcher resort to the postulates, if it were not for writing a bestseller (... any single formula in a book reduces the paid circulation by ... (unknown source)). Isn't this unencyclopedic, a la textbook? ;)
• Apologies for my off topic curiosity: I know about the constructs of gerunds and infinitives, and I learned back then that "allow" could be used with both constructs (in contrast to "allow for", which is only to be used with the gerund). Was this wrong all the time, has it changed some time in between, or is it a matter of taste? Ignore, if bothering. Thanks.

As usual, something to wholeheartedly disagree to. :) Purgy (talk) 20:19, 23 November 2018 (UTC)

Time Dilation

Before

Time dilation explains a number of physical phenomena; for example, the (expected) lifetime of a muon that starts to exist with a collision of a cosmic ray with a particle of the Earth's atmosphere, then moves at very high speed towards the surface, and decays near there, is measured as greater than the lifetimes of slowly moving muons, generated and decaying in a laboratory. Both muons would, of course, measure identical lifetimes, when looking at their respective wrist watches, and both observe the other as moving, and the moving watch as ticking slower than their own, which is said to show the proper time, as measured by an observer (at rest in its frame).

After

Time dilation explains a number of physical phenomena; for example, the lifetime of high speed muons created by the collision of cosmic rays with particles in the Earth's outer atmosphere and moving towards the surface is greater than the lifetime of slowly moving muons, created and decaying in a laboratory.

Commentary

Both JRSpriggs and I worked on this one. We halved the number of words and simplified sentence structure. Measuring "(expected) lifetime of a muon" is easily misread from what you apparently intended.

Dragging effects

Rindler states, on page 54 of his textbook, "From the point of view of special relativity, however, the result (3.1) is nothing but the relativistic velocity addition formula!" He doesn't even use the word "composition." All of the "delicate" nuances that you insist on should already be implied and understood from previous explication of the relativistic composition of velocities, and should not clutter discussion of dragging effects.

Standard configuration

Shorthand expression "standard configuration" reduces a lot of verbiage. The expression is repeatedly used not just in my writing, but in the legacy "Technical discussion of spacetime" section containing material that I judged to be beyond freshman-sophomore mathematics level. If you wish to start with showing the boost-equations in (1+1) dimensions, generalize to (1+3) dimensions in matrix notation, and reduce the matrix again to "standard configuration" etc. etc. , then you should draft a section for the technical section. It's there for a reason. It sounds to me like your proposal could be a great addition.

Two postulates

You appear to misunderstand my rewording of the section titles. Historically, this article appears to have been written by two camps of editors, a group of "two-postulates" advocates, and a group of "single postulate of Lorentz invariance" advocates. When I started my series of edits, the article was a mishmash of contributions by the two groups, and was very confusing to me, until I understood the historical development of this article. I am a "packrat" and do not like throwing out material. Rather than delete legacy "two-postulates" material, what I am trying to say with my rewording of the section titles is: Traditionally, special relativity has been presented in terms of Einstein's two postulates. This article does not follow this old tradition, but instead presents special relativity using the single postulate of Lorentz invariance.

Use of "allow"

You are referring, I presume, to this edit. "Allow to deal with" is wrong, and this wrongness is not a matter of taste. You can write, "allow one to deal with" or "allow dealing with".

General comment

Please use diffs to pinpoint problematical edits. Otherwise you force me to do a lot of research to pinpoint the exact phrase that you have having issues with. Prokaryotic Caspase Homolog (talk) 12:28, 24 November 2018 (UTC)

Purgy's reply

Thanks for the grammar, apologies for missing links, Roma locuta, ... We are the faithful. Nevertheless, a few remarks:

- no high speed muons, no equal lifetime in specific frames?

- I did not refer at all to "Dragging effects", I experience the content of this section as delicate. I seriously protest against calling the "transformation" of a velocity from one frame to another frame an "addition", not even a composition, just because the transformation in the Galilean transform is represented by an addition. Velocities are never added, the are transformed in a Galilean setting by simply adding a quantity, which is characteristic for the transformation, and necessarily must be of equal dimension $Ls^{-1},$ and in a more complex way in STR spacetime. Of course, the transformation, as all LT do, involves a velocity, but I would avoid calling this even a composition. As usual: just to let you know.

- I would prefer not to. Bartleby's English is not firm enough to compose a full section.

- Obviously I am not sufficiently sensitive to experience the nuances of the two sources, or I was trained to ignore all postulate driven derivations after having seen the derivation of the full blown LT from first principles, presented by a real Grandmaster of the Chalk (sort of a W. Lewin, if this is allowed to state wrt lecture quality).

I am around, hopefully not disturbing. Purgy (talk) 18:40, 24 November 2018 (UTC)

Not obvious?

Never would I simply revert this edit, but ...

- Given two frames in standard configuration (unprimed, primed),

- and having derived that the parameters $v$ and $v'$ of the respective Lorentz transformations of coordinates between these frames, both parameters representing measurements in the respective frames, satisfy the equation $v'=-v$ in this configuration,

- and having also derived how a velocity $a$ transforms under Lorentz transform with parameter $w$ (denoted ${\mathcal {L}}_{w}$) to $b={\mathcal {L}}_{w}(a),$ specifically $u'={\mathcal {L}}_{v}(u)={\frac {u-v}{1-uv/c^{2}}}$ and $u={\mathcal {L}}_{v'}(u')={\frac {u'-v'}{1-u'v'/c^{2}}},$

- then -using the equation of the premise- $\qquad u={\frac {u'+v}{1+u'v/c^{2}}}={\text{“}}{\mathcal {L}}_{v}^{-1}(u'){\text{”}}.$

To me the above conclusion in the last step is immediate/obvious/..., but I see no reasoning that to achieve an inverse of a Lorentz transform

- primed and unprimed symbols are interchanged and a parameter is replaced by its negative,

(both recipes only motivated by the structure of two formulae?), but rather this is coherently done by

- performing an appropriate Lorentz transform (from all primed to unprimed), and then

- substituting the derived parameter identity.

BTW, my editorializing term of velocities being incoherent, if they belong to different frames, is based on the fact that in the inverse Lorentz transformation the parameter velocity and the transformed velocity are derivatives with respect to a different time. This reservation also holds for transforming simple coordinates. Validity of any replacements must be justified for each installment. Purgy (talk) 10:32, 4 January 2019 (UTC)

Remember, I consider the primary target audience for the first half of this article to be lower division college science students and senior high school students. Many of your contributions tend to be detailed to the point of being incoherent to the target audience, although entirely appropriate for the second, "technical" half of the article.

If a lower division college science student asks me what a good book for self-study would be, I would recommend Morin or French. I desire the first half of the article to be at the level of those textbooks.

You can be as detailed and precise as you want in the "technical" half of the article.

Prokaryotic Caspase Homolog (talk) 12:25, 4 January 2019 (UTC)

Emission theory of light

The normal introductory dialog on relativity says "No aether could be found so there must be constant speed of light", and then we change basic constructs of time and space to fit. But the much more obvious explanation is the Emission theory. It occurred to me as a student, and to Newton long before that. And the binary star refutation was not produced until long after relativity, and Fox's refutation of that much later.

I believe this warrant some solid introductory text. Otherwise it simply does not make sense to anyone that does not already understand it. And it encourages the worst type of thinking in the sciences, merely repeating what authoritative people say without thinking about it.Tuntable (talk) 00:51, 4 April 2019 (UTC)

Next steps

New sections under consideration

After adding the section on Graphical representation of the Lorentz transformation, it became possible for me to move Causality and prohibition of motion faster than light from where it had been stuck to a more rational location in the article, and then to fence off the old legacy sections behind a "Warning! There be lions and tigers and bears (oh my) beyond this point!" sign.

There is obviously a lot left to be done. Optical effects ought to include relativistic aberration and maybe the Fizeau experiment??? Dynamics, of course, covers force, energy and momentum, collisions, and relativistic mass (and why the majority of physicists consider it to be a deprecated concept). Relativistic mass is a concept that most lay persons have heard about, and I'm sure that many visitors to this article page have been disappointed not seeing any mention of it.

I'm hoping that my reorganization should make it easier to add these additional topics. Prokaryotic Caspase Homolog (talk) 09:33, 11 November 2018 (UTC)

Hmmm... it looks like I need to cover the magnet and conductor thought experiment as a preparatory step before covering relativistic aberration. Prokaryotic Caspase Homolog (talk) 06:48, 18 November 2018 (UTC)

Should experimental results be blended with the main narrative or kept separate?

Currently, almost all discussion of the experimental justification for SR is sequestered in the Status section, not that there is very much of it.

Is this a desirable organization? Prokaryotic Caspase Homolog (talk) 20:49, 14 November 2018 (UTC)

Suggestion to extend the section on relativity and quantum mechanics

I would recommend to add to that section a mentioning of the Thomas precession. An extremely clear, though still elementary, introduction to this effect is provided in the excellent textbook by Stepanov.Efroimsk (talk) 04:43, 10 September 2019 (UTC)

Pre-relativistic understanding of length contraction and time dilation

@JRSpriggs: Please comment on the proposed revised statement+notes+references and suggest changes as necessary. Prokaryotic Caspase Homolog (talk) 07:47, 15 November 2018 (UTC)

• I had written the following:

In pre-relativistic physics, distance and time were considered to be independent measurements, and despite some puzzling experimental results, physicists had no inclination to believe that measured distance or time between events should change as a result of a shift in frame from which measurements are made.

• You commented, "distance between events DOES change in prerelativistic physics as a result of a change in the reference frame, unless the time of the events is the same" and changed the wording to the following:

In pre-relativistic physics, distance and time were considered to be independent measurements, and despite some puzzling experimental results, physicists had no inclination to believe that measured time between events should change as a result of a shift in frame from which measurements are made.

• Pre-relativistic views of length contraction and time dilation are rather complex to describe, and my initial phrasing was an (apparently futile) attempt to avoid going into extensive discussion of Lorentz's and Poincaré's speculations. I propose the following revision with notes and references:

In pre-relativistic physics, distance and time were considered to be independent measurements, and despite some puzzling experimental results, physicists had no inclination to believe that any "true" measured distance or time between events should change as a result of a shift in frame from which measurements are made.

• I am quite aware that the final form of Lorentz ether theory predicts, within its domain of applicability, results which are identical to those of special relativity. LET, however, underwent extensive development between 1892 through 1905, and meant quite different things at different times. Just because the final form of the theory does not contradict Newton's third law, does not invalidate my statement in the notes that earlier versions had difficulties in conforming with classical mechanics.

Notes

Primary sources

References

• You are over-thinking this. I was not talking about length contraction or any such thing. The sentence which I changed said "... measured distance or time between events should change as a result of a shift in frame ..." (emphasis added). Before special relativity, we had Galilean relativity according to which the transformation law for frames of reference was:

${\begin{aligned}t'&=t\\x'&=x-vt\\y'&=y\\z'&=z,\end{aligned}}$.

The "− v t" term means that the location of an event depends on the time that its position is measured. So if you subtract two such locations to get the x-component of the distance, you will get a value which depends on the times of the events. That is my whole point. JRSpriggs (talk) 20:10, 15 November 2018 (UTC)

Well, that does not represent what Purgy and I intended. Will have to do a major re-write. Prokaryotic Caspase Homolog (talk) 23:49, 15 November 2018 (UTC)

More precisely one could perhaps write about coordinatizing two events

${\text{E}}_{i},\quad i\in \{1,2\}$

in two Galilean $(t'=t;\;x'=x-vt;\;y'=y;\;z'=z)$ inertial frames in standard configuration

$E_{i}\mapsto \{(t_{i},x_{i},y_{i},z_{i}),\;(t'_{i},x'_{i},y'_{i},z'_{i})\},$

leaving separately both their time lapse

$\Delta t=t_{2}-t_{1}=t'_{2}-t'_{1}$

and their contemporal $(t_{1}=t_{2})$ spatial distance

$\Delta r^{2}=(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}=(x'_{2}-x'_{1})^{2}+(y'_{2}-y'_{1})^{2}+(z'_{2}-z'_{1})^{2}$

invariant.

Not talking about the boring coordinates, this could be also more detailed to

$\Delta r=r_{2}-r_{1}=(r_{2}-vt_{2})-(r_{1}-vt_{1})=r'_{2}-r'_{1}.$

The space—time interweaving puts an end to identical time as well as to contemporality across non comoving frames. Sorry, I missed from the diff-view the suggestion below, and also had no edit conflict. Use to your liking. Purgy (talk) 09:17, 16 November 2018 (UTC)

---

• Let's try this:

In Galilean relativity, length ($\Delta r$) and temporal separation between two events ($\Delta t$) are independent invariants, the values of which do not change when observed from different frames of reference.

In special relativity, however, the interweaving of spatial and temporal coordinates generates the concept of an invariant interval, denoted as $\Delta s^{2}$:

$\Delta s^{2}\;{\overset {def}{=}}\;c^{2}\Delta t^{2}-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2})$

The interweaving of space and time revokes the implicitly assumed concepts of absolute simultaneity and synchronization across non-comoving frames.

Notes

Primary sources

References

• This edit rephrased the footnote defining "length" as a prima vista triviality. A prominent intent in me writing a "bulky" definition for this everyday notion was to introduce the notion of events in their fundamental role of establishing "length", the value of which will turn out as varying from frame to frame, because of varying coordinates of these events. I think the ladder paradox is directly connected here, and a caveat of carrying forward a sloppy notion of length into the realm of STR is appropriate. Purgy (talk) 11:10, 17 November 2018 (UTC)

I know what you meant, but I found your original wording confusing. "In a spacetime setting the length of a rigid object is defined by the spatial distance of the two events made up of the ends of this object at the same time." The ends of the object are not events, but follow world lines. So you intended that the length of the object should mean the spatial distance between two events, having the same time coordinates, selected from the world lines of the two ends. This spatial distance would, in general, be less than the length measured in the rest frame of the object (i.e. its proper length). In the rest frame of the object, however, it is not at all necessary that the selected events have the same time coordinate.

All this amounts to a lot of superfluous detail, especially in a footnote for the Galilean scenario for which length is an invariant. Prokaryotic Caspase Homolog (talk) 13:45, 17 November 2018 (UTC)

To me an end of an object at some point in time makes up a perfect event ("two events made up of the ends of this object at the same time"), and varying time traces out a world line, which is a certain collection of events; and I perceive no problem with getting acquainted to the notion of a time-varying lenght, as observed from different frames, never getting longer than some distinguished length, one might call a proper length. I do not know how fruitful it is to continue measuring lengths at different times, which only works in the rest frame of the object, and I expressed my doubts about leaving the notion of length in its "trivial" setting of Galileian spacetime.

I did not suggest a footnote pertaining to the Galileian notion of length, but a footnote to a sustainable notion of length in general, and to focus the attention to the upcoming change in the notion of length. I think the method of "how to measure length" should not be changed/restricted during migration to STR, and thus I am unaware of a "lot of superfluous detail", however, I consider a footnote, missing to warn about the upcoming subtleties, to be really superfluous. Lifting the wording above confusion (which I miss) to your standards is beyond me, disagreeing is not. :) Purgy (talk) 17:01, 17 November 2018 (UTC)

In terms of English language usage,

• I do not know what a "spatial distance of two events" means. I do know what a spatial distance between two events means.
• I do not know what "two events made up of the ends of the object at the same time" means. I do know what two "ends of the object measured at the same time" means.
• Applying the two "Englishian phrase transformations" essentially converts one phrase to the other, except for your use of "is defined by."

Prokaryotic Caspase Homolog (talk) 18:33, 17 November 2018 (UTC)

An apology for lack in English idiomology is certainly nonsensical, I just regret it. In German the use of a genitive ("of") instead of a preposition ("between") is common habit, I do ask for improving my construction of "making up" events from their spatial and temporal coordinates (but leaving "events" in place), while talking about their "spatial distance", and, thirdly, after applying the EPT (see above) I do miss not only the rigor-effusing "is defined by", but also the mentioned "event", which is at the heart of post-Galilean spacetime.

I repeat the heart of my complaint: "prima vista triviality". If it were not for the last, innocuously sounding phrase ("measured at the same time"), the whole footnote would be absolutely "superfluous". My concern is to transport to the reader this essential condition not as a small closing phrase, but as an essential, concept transforming information, and I tried to do this via the demonstrative use of "defining" and "event". As usually, take what you like. Purgy (talk) 21:13, 17 November 2018 (UTC)

No, it is not trivial. It is at the heart of the "brain freeze" that led to my oversight. I should have known better. I thank JRSpriggs for correcting me, and I thank you for introducing the original version of the footnote.

Pushed to main space. We can work on improving it later, but there are other topics to add. Prokaryotic Caspase Homolog (talk) 04:19, 18 November 2018 (UTC)

I am afraid of being misunderstood. I never wanted to state that the footnote, as is stands now, were trivial. I want to express my perception that its current formulation lacks emphasis on the changing settings in Galilean and -say- Einsteinian spacetime. To my taste, it evokes a prima vista(=sometimes wrong!)-impression of not being that fundamental as it is, by putting a condition, generating the decisive difference, into a small appendix of the sentence. My pleadings just ask for more emphasis on the change, suggesting the use of the words "define" and "event". There is absolutely no need, for a statement to be correct, of conforming to my taste. Purgy (talk) 09:24, 18 November 2018 (UTC)

I didn't go Deep Into the emission Theory but some of its starting lines say that light is emitted by a speed 'C' relative to the source which is indeed not true as experiments Would see that the speed of light won't increase if emitted from a moving object or from one at rest Om C Thorat (talk) 16:17, 23 January 2020 (UTC)

"Intuition" in interpreting spacetime diagrams

@UKER: objected to the analogy used here, calling the analogy "childish":

While the unprimed frame is drawn with space and time axes that meet at right angles, the primed frame is drawn with axes that meet at acute or obtuse angles. The frames are actually equivalent. The asymmetry is due to unavoidable distortions in how spacetime coordinates map onto a Cartesian plane. By analogy, planar maps of the world are unavoidably distorted, but with experience, one learns to mentally account for these distortions.

Uker replaced it with the following wording

While the observer frame is represented with space and time axes that meet at right angles, the axes for observers in different frames of reference are represented with their axes meeting at acute or obtuse angles. This unavoidable asymmetry stems from the way spacetime coordinates map onto a Cartesian plane, but it should not affect the intuition that all the represented frames of reference are equivalent.

It is not an "intuition" that all represented frames of reference are equivalent. Their equivalence is a fact, and recognition of their equivalence is not a native intuition, but rather is an element of knowledge that comes with experience.

Proposed compromise, removing the analogy, but correcting the introduced error of fact.

While the unprimed frame is drawn with space and time axes that meet at right angles, the primed frame is drawn with axes that meet at acute or obtuse angles. The frames are actually equivalent. The asymmetry is due to unavoidable distortions in how spacetime coordinates map onto a Cartesian plane, but with experience, one learns to mentally account for these distortions.

Prokaryotic Caspase Homolog (talk) 12:24, 3 August 2020 (UTC)

UKER's "the observer frame" sounds ambiguous. I'd prefer the first sentence of your version:

"While the unprimed frame is drawn with space and time axes that meet at right angles, the primed frame is drawn with axes that meet at acute or obtuse angles. The frames are equivalent."

We don't need the pedagogic remark. But as always, to avoid this kind of back and forth, stick a good source to it and cast it in concrete. - DVdm (talk) 12:47, 3 August 2020 (UTC)

I can agree with the primed/unprimed syntax. My issue, as DVdm says, is that comparison to cartographical maps, which seems targeted at a much lower level demographic than the whole rest of the article. --uKER (talk) 21:09, 3 August 2020 (UTC)

The cartographical analogy is quite commonly used in describing spacetime diagrams, but I can understand why you do not think it appropriate. The learning "to mentally account for these distortions" is a paraphrase of Schutz, but including an actual reference to Schutz seems to be going too far. Overall, I think my proposed compromise should give us each half of what we want, leaving us each a bit disappointed that we didn't get all of what we want. That's the whole point of compromise, after all. Prokaryotic Caspase Homolog (talk) 21:48, 3 August 2020 (UTC)

Ha, Schutz. Bring him on in a reference and let's close this . - DVdm (talk) 21:50, 3 August 2020 (UTC)

Hmmm... "The prohibition against OR means that all material added to articles must be attributable to a reliable, published source, even if not actually attributed." When I look at the original section in Schutz,

I see discussion on various features of spacetime diagrams that take getting used to, illustrating the "inappropriateness of using geometrical intuition based on Euclidean geometry....[the student] has to adapt his intuition accordingly." Strictly speaking, a citation would be WP:SYN of separate sentences by a single author. Prokaryotic Caspase Homolog (talk) 06:13, 4 August 2020 (UTC)

OK, we can leave it out. No big deal... - DVdm (talk) 08:33, 4 August 2020 (UTC)

I saw your edit, but that sentence was cringe inducing in that it was written in what seemed like a pedantic-sounding first person, like saying "I'm so experienced I can mentally interpret them properly". Do we really need that remark? What value does it provide? Communicating the article's reader that there's people that can actually read the diagram despite some minor geometric incovenience? --uKER (talk) 02:19, 6 August 2020 (UTC)

I'm OK with these latest changes of yours. It's only your ORIGINAL attempt at rewording that I had serious objections to. "It should not affect the intuition that all the represented frames of reference are equivalent" made me cringe. Prokaryotic Caspase Homolog (talk) 04:36, 6 August 2020 (UTC)

Fair enough. Give it your best shot. :) --uKER (talk) 05:36, 6 August 2020 (UTC)